Secondary battery system, secondary battery, and assembled battery system

ABSTRACT

According to an embodiment, a secondary battery system includes a secondary battery, a calculator, and a controller. The secondary battery includes a first electrode including a first and second active materials, and a second electrode including a third active material. The calculator calculates a current ratio of currents passing through the first and second active materials for each of different values of a charge amount of the first electrode, based on capacities and capacity-versus-potential properties of the first and second active materials. The controller, based on the capacities of the first and second active materials and the current ratio when the charge amount of the first electrode takes a first value, controls the current passing through the secondary battery when the charge amount indicates the first value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromJapanese Patent Application No. 2019-043439, filed Mar. 11, 2019, theentire contents of which are incorporated herein by reference.

FIELD

Embodiments described herein relate generally to a secondary batteryhaving electrodes prepared from a mixture of multiple active materials.

BACKGROUND

Recently, as the prevalence of electronic devices includinginformation-related devices and communication devices increases, so toodoes the prevalence of secondary batteries that serve as a power supplyto such devices. Secondary batteries are also advancing in popularity inthe fields of electric vehicles (EV) and renewable energy. Particularly,a lithium-ion secondary battery has been broadly used because of itshigh energy density and easiness of being downsized.

The lithium-ion secondary battery charges and discharges electric energywith the active material of the cathode and anode absorbing andreleasing lithium ions. Specifically, at the time of charging, lithiumions released from the cathode are absorbed by the anode, whereas at thetime of discharging, lithium ions discharged from the anode are absorbedby the cathode.

The electrodes, or in other words, cathodes and/or anodes, of typicallithium-ion secondary batteries are formed using a single activematerial. For the purposes of increased capacity and increased lifespan,electrodes prepared from a mixture of active materials of multiple typesmay be used. Such electrodes may exhibit complex properties incomparison to electrodes formed from a single active material. Dependingon the capacity region of the battery for use, the amount of chargingand/or discharging current for the battery, or the like, deteriorationof the secondary battery may be increasingly advanced.

In a known conventional technique, for example, when a cathode activematerial having a relatively small capacity ratio is mainly undergoingcharging reaction, the charge current is set to a smaller value thanwhen a cathode active material having a relatively large capacity ratiois mainly undergoing charging reaction.

With the conventional technique, however, which of one active materialand the other active material is undergoing the charging reaction and towhat extent cannot be accurately estimated. For example, a load on anactive material may largely differ when this active material is almostsolely undergoing the charging reaction, from when the active materialis undergoing charging reaction slightly more than the other activematerial. For this reason, even if a cathode active material having arelatively small capacity ratio is mainly undergoing charging reaction,the charge current may not have to be considerably restricted dependingon the degree of charging reaction. In contrast, even if a cathodeactive material having a relatively large capacity ratio is mainlyundergoing charging reaction, the charge current may need to beconsiderably restricted depending on the degree of charging reaction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing a secondary battery system accordingto the first embodiment.

FIG. 2 is a graph showing the capacity-versus-potential properties oftwo different active materials.

FIG. 3 is a graph showing the capacity-versus-potential properties ofcathodes prepared by mixing the active materials of FIG. 2 in differentmixture ratios.

FIG. 4 is a graph showing a current ratio between the active materialsin each of the cathodes of FIG. 3.

FIG. 5 is a graph showing the substantial charging rate of each of theactive materials when charging the secondary batteries including thecathodes of FIG. 3 at constant rate.

FIG. 6 is a graph showing the charge current control in accordance withFIG. 5.

FIG. 7 is a graph showing the charge current control of the cathodesprepared by mixing the active material A and the active material B inthe ratio of 1:1.

FIG. 8 is a flowchart showing the operation of the secondary batterysystem illustrated in FIG. 1.

FIG. 9 is a block diagram showing a secondary battery system accordingto the second embodiment.

FIG. 10 is a diagram showing a circuit model of a target electrode usedin the secondary battery system according to the fourth embodiment.

FIG. 11 is a graph showing the current ratio between the activematerials in each of the electrodes of FIG. 3 calculated in accordancewith the model of FIG. 10.

FIG. 12 is a block diagram showing the secondary battery systemaccording to the fifth embodiment.

FIG. 13 is a flowchart showing the operation of the secondary batterysystem illustrated in FIG. 12.

DETAILED DESCRIPTION

According to an embodiment, a secondary battery system includes asecondary battery, a current ratio calculator, and a controller. Thesecondary battery includes a first electrode including a first activematerial and a second active material, and a second electrode includingat least a third active material. The current ratio calculatorcalculates a current ratio of a current passing through the first activematerial and a current passing through the second active material foreach of different values of a charge amount of the first electrode,based on a capacity and capacity-versus-potential properties of thefirst active material and a capacity and capacity-versus-potentialproperties of the second active material. The controller, based on thecapacity of the first active material, the capacity of the second activematerial and the current ratio when the charge amount of the firstelectrode takes a first value, controls the current passing through thesecondary battery when the charge amount of the first electrodeindicates the first value.

According to another embodiment, a secondary battery system includes asecondary battery, a current ratio calculator, and a controller. Thesecondary battery includes a first electrode including a first activematerial and a second active material, and a second electrode includingat least a third active material. The current ratio calculatorcalculates a current ratio of a current passing through the first activematerial and a current passing through the second active material foreach of different values of a charge amount of the first electrode,based on a capacity and capacity-versus-potential properties of thefirst active material and a capacity and capacity-versus-potentialproperties of the second active material. The setter sets an operationalrange of the secondary battery based on the capacity of the first activematerial, the capacity of the second active material, and the currentratio.

According to still another embodiment, a secondary battery includes afirst electrode and a second electrode. The first electrode includes afirst active material and a second active material. The second electrodeincludes at least a third active material. An initial charge amount ofthe second electrode is larger than an initial charge amount of thefirst electrode. In at least part of a range in which the charge amountof the first electrode is smaller than the initial charge amount of thesecond electrode, a product of (a) a first ratio of a current passingthrough the first active material to a current passing through the firstelectrode, (b) a reciprocal of a second ratio of a capacity of the firstactive material to a capacity of the first electrode, and (c) aconstant, exceeds a threshold value.

According to still another an assembled battery system includes anassembled battery, an internal state calculator, a current ratiocalculator, and a controller. The assembled battery includes a pluralityof secondary batteries coupled in parallel or in series. Each of thesecondary batteries includes a first electrode including a first activematerial and a second active material, and a second electrode includingat least a third active material. The internal state calculator performsregression calculation for each of a plurality of battery modulesobtained by dividing the secondary batteries, based on input dataincluding at least one of (a) measurement values of currents and/orpowers measured at a plurality of time points during charging and/ordischarging each battery module and (b) estimated values of currentsand/or powers at a plurality of time points during charging and/ordischarging the battery module, and to update a capacity of the firstactive material of the secondary battery included in the battery moduleand a capacity of the second active material of the secondary battery.The current ratio calculator calculates for each of the battery modulesand for each of different values of a charge amount of the firstelectrode of the secondary battery included in the battery module acurrent ratio of a current passing through the first active material ofthe secondary battery and a current passing through the second activematerial of the secondary battery, based on the capacity andcapacity-versus-potential properties of the first active material of thesecondary battery and the capacity and capacity-versus-potentialproperties of the second active material of the secondary battery. Thecontroller determines a recommended current rate, for each of thebattery modules, for charging and/or discharging the battery module whenthe charge amount of the first electrode of the secondary batteryincluded in the battery module takes a first value, based on (a) thecapacity of the first active material of the secondary battery, (b) thecapacity of the second active material of the secondary battery, and (c)the current ratio when the charge amount of the first electrode of thesecondary battery takes the first value, and to control a currentpassing through the assembled battery, based on the recommended currentrate determined for each of the battery modules.

The embodiments will be described below with reference to the drawings.The same or similar reference numerals are applied to the componentsthat are the same as or similar to the explained components, andrepetition of explanations made before is basically avoided. Thedrawings are schematically or conceptually illustrated, and thereforethe relationship between the thickness and width of each illustratedcomponent and relative sizes of the components may not be the same asthe actual arrangement. Furthermore, even if the same portion isdescribed, it may be illustrated differently in sizes and ratios ondifferent drawings.

First, the battery capacity and state of charge (SOC) in thisspecification will be defined. In general, the capacity of a lithium-ionsecondary battery is calculated based on an upper limit voltagedetermined at the time of charging and a lower limit voltage determinedat the time of discharging.

In this specification, however, the capacity of a secondary battery isdefined with reference to the open circuit voltage (OCV) of thesecondary battery. Specifically, the capacity of the secondary batteryis defined as the charging capacity at the time of charging thesecondary battery until the OCV changes from the predetermined lowerlimit voltage to the predetermined upper limit voltage, or as thedischarging capacity of the secondary battery at the time of dischargingthe secondary battery until the OCV changes from the upper limit voltageto the lower limit voltage.

Throughout the specification, the SOC of a secondary battery representsthe ratio of the charge amount of the secondary battery to the capacityof the secondary battery when the OCV at the lower limit voltage is0[%], and the OCV at the upper limit voltage is 100[%].

Throughout the specification, the SOC of the cathode of the secondarybattery represents the ratio of the cathode charge amount to thecapacity of the cathode when the open circuit potential (OCP) of thecathode at the lower limit potential is 0[%], and the OCP at the upperlimit potential is 100[%].

Similarly, throughout the specification, the SOC of the anode of thesecondary battery represents the ratio of the anode charge amount withreference to the capacity of the anode when the OCP of the anode at thelower limit potential is 0[%], and the OCP at the upper limit potentialis 100[%].

First Embodiment

A secondary battery system according to the first embodiment includes abattery control apparatus 100, a secondary battery 110, a load/powersource 120, a current measurer 130, and a voltage measurer 140, asillustrated in FIG. 1.

A typical secondary battery 110 is a lithium-ion secondary battery. Thecharging and discharging of the secondary battery 110 may be controlledby the battery control apparatus 100. The secondary battery 110 iscoupled to the load/power source 120 at the time of discharging orcharging.

The secondary battery 110 includes a cathode and an anode. At least oneof the cathode and the anode contains different active materials. In thefollowing explanation, it is assumed that the cathode contains twoactive materials that are an active material A and active material B.Here, the active material A is spinel-type lithium-manganese compositeoxide (LMO), and the active material B is lithium-nickel composite oxide(NCA, NCM). The present embodiment and later-described embodiments arealso applicable to a cathode containing a combination of differentactive materials, and to an anode containing different active materials.

The current measurer 130 may be an ammeter. The current measurer 130measures the current (battery current) passing through the circuitincluding the secondary battery 110 and the load/power source 120, andoutputs a signal indicating the current measurement value to the batterycontrol apparatus 100.

The voltage measurer 140 may be a voltmeter. The voltage measurer 140measures a voltage (battery voltage) applied to the two ends of thesecondary battery 110, and outputs a signal indicating the voltagemeasurement value to the battery control apparatus 100.

The structure may be further provided with a temperature measurer thatmeasures the temperature of the secondary battery 110 or ambienttemperature, although it is not shown.

The battery control apparatus 100 may correspond to a processor and amemory. Typical examples of the processor may be a central processingunit (CPU) and/or graphics processing unit (GPU); however, the examplesmay also include a microcomputer, a field programmable gate array(FPGA), a digital signal processor (DSP), or any other general-purposeprocessor or a dedicated processor.

The memory temporarily stores programs to be implemented by theprocessor to realize the process related to battery control, and data tobe used by the processor, such as various measurement values, internalstate parameters, and mathematical functions. The memory may include arandom access memory (RAM) that has a work area for expanding a programor data.

The battery control apparatus 100 calculates the current ratios of thecurrents passing through different active materials in the targetelectrode (e.g., cathode) of the secondary battery 110 under differentcharge amounts (or SOCs) of the electrode of the secondary battery 110.Based on the relationship between the charge amount and the currentratio, the battery control apparatus 100 controls the current passingthrough the secondary battery 110 so that, for example, the chargingrate and/or discharging rate of the secondary battery 110 can be reducedin a certain charge amount region.

In particular, the battery control apparatus 100 includes a currentratio calculator 101 and a charge/discharge controller 102.

The current ratio calculator 101 calculates the current ratios betweenthe active material A and the active material B under different chargeamounts of the secondary battery 110, based on the capacities of theactive material A and active material B and theircapacity-versus-potential properties. Thereafter, the current ratiocalculator 101 sends the calculated current ratio to thecharge/discharge controller 102. It is assumed that the capacities ofthe active material A and/or active material B are predetermined. Thecapacities, however, may be estimated and updated in accordance with thedeterioration of the secondary battery 110 that gradually advances, asexplained in the later described fifth embodiment.

The capacity of the active material A is set as Ma[g], and the capacityof the active material B is set as Mb[g]. Examples of thecapacity-versus-potential properties include a function fa( ) thatreturns the potential (OCP) of the active material A with a chargeamount per unit mass of the active material A as an argument, and afunction fb( ) that returns the potential (OCP) of the active material Bwith a charge amount per unit mass of the active material B as anargument. These functions are predetermined from experiments orsimulations, and stored in the memory. Instead of the functions, curvedata or a look-up table (LUT) may be stored.

These functions fa( ) and fb( ) are exemplified in FIG. 2. In FIG. 2,the function fa( ) is plotted as a curve A, and the function fb( ) isplotted as a curve B. Furthermore, the functions for returning thepotential (OCP) of the cathode from the charge amount per unit mass ofeach cathode when the mixture ratios between the active material A andactive material B are 10:0, 8:2, 6:4, 4:6, 2:8 and 0:10, are exemplifiedin FIG. 3. If the mixture ratio is 10:0 or 0:10, the function will bethe same as function fa( ) or fb( ), respectively, in FIG. 2. In thefollowing explanation, the mixture ratio denotes a ratio of masses,unless otherwise specified.

The potential of the active material A is equal to the potential of thecathode, and the potential of the active material B is also equal to thepotential of the cathode. This means that the potential of the activematerial A is equal to the potential of the active material B. As aresult, the following equation (1) is established.

$\begin{matrix}{{{fa}\left( \frac{Qa}{M\; a} \right)} = {{fb}\left( \frac{Qb}{Mb} \right)}} & (1)\end{matrix}$

In equation (1), Qa and Qb each denote the charge amount of the activematerial A and the charge amount of the active material B when thecharge amount of the cathode is Q. Although Qa and Qb are unknown, thesum of Qa and Qb is equal to Q.

Since equation (1) contains a single unknown number as indicated below,the current ratio calculator 101 can identify the combination of Qa andQb that satisfies equation (1), for example, from numerical computation.

$\begin{matrix}{{fa}{\left( \frac{Qa}{Ma} \right) = {f{b\left( \frac{Q - {Qa}}{Mb} \right)}}}} & (2)\end{matrix}$

Supposing that a charge/discharge current is passed over a short timeperiod Δt, the charge amount of the cathode changes from Q to Q+iΔt.Concurrently, the charge amount of the active material A changes from Qato Qa+iaΔt, and the charge amount of the active material B changes fromQb to Qb+ibΔt. Here, ia and ib denote the sizes of currents that passthrough the active material A and active material B, respectively,during the short time period Δt. The ratio ia:ib denotes the currentratio calculated by the current ratio calculator 101.

The following equation (3) is derived by the first order approximation.

$\begin{matrix}{{{{fa}\left( \frac{Qa}{Ma} \right)} + {\frac{ia\Delta t}{Ma}{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}}} = {{f{b\left( \frac{Qb}{Mb} \right)}} + {\frac{ib\Delta t}{Mb}{fb}^{\prime}\;{\left( \frac{Qb}{Mb} \right).}}}} & (3)\end{matrix}$

In equation (3), fa′( ) and fb′( ) are derivatives of functions fa( )and fb( ), respectively. The data (or alternatively, curve data or LUT)of derivatives fa′( ) and fb′( ) may be pre-calculated and stored in thememory. Equation (3) can be simplified as follows, by using the aboveequation (1):

$\begin{matrix}{{\frac{ia\Delta t}{Ma}{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}} = {\frac{ib\Delta t}{Mb}{{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}.}}} & (4)\end{matrix}$

Although ia and ib are unknown, the sum of ia and ib is equal to i.Thus, ib=i−ia is established. By substituting this to equation (4),equation (5) is derived as indicated below.

$\begin{matrix}{\frac{ia}{i} = \frac{{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}Ma}{{{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}{Mb}} + {{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}Ma}}} & (5)\end{matrix}$

Because ib=i−ia, the following equation (6) is established.

$\begin{matrix}{\frac{ib}{i} = \frac{{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}Mb}{{{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}Mb} + {{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}Ma}}} & (6)\end{matrix}$

In view of the above, the current ratio calculator 101 simply needs tocalculate the current ratio represented in equation (7).

$\begin{matrix}{{{ia}\text{:}{ib}} = {{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}{Ma}\text{:}{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}{Mb}}} & (7)\end{matrix}$

When the current ratios are calculated in the above manner for thecathodes having different mixture ratios as exemplified in FIG. 3, thegraph of FIG. 4 can be obtained. Although FIG. 3 includes OCP curves forthe cathodes having mixture ratios of 10:0 and 0:10, these electrodesare not mixed electrodes. In other words, the current always passesthrough a single active material. Thus, these cathodes are omitted fromthe explanation.

By referring to FIG. 4, regardless of the mixture ratio of the cathode,the current passes mainly through the active material B in the low-SOCregion of the cathode, while the current passes mainly through theactive material A in the high-SOC region of the cathode (approximatelyup to 85%). However, the range of SOC of the cathode within which thecurrent ratio with respect to each active material increases largelydepends on the mixture ratio of the cathode. For example, if the mixtureratio of the active material A to the active material B is 8:2, thecurrent passes mainly through the active material. B in the range of theSOC of the cathode approximately between 0[%] and 25[%], and through theactive material A in the range of the SOC approximately between 25[%]and 95[%]. On the other hand, if the mixture ratio of the activematerial A to the active material B is 2:8, the current that passesthrough the active material A is slightly larger than the current thatpasses through the active material B in the range of the SOC of thecathode approximately between 70[%] to 85[%], and the current passesmainly through the active material B in the remaining range.

The battery control apparatus 100 may receive from the current measurer130 a signal indicating the current measurement value every unit time,and perform time integration on the current measurement value toestimate the charge amount of the secondary battery 110. The functionalblock that performs this operation may be referred to as a batterycharge amount estimator.

The battery control apparatus 100 can estimate the charge amount of thecathode by adding the initial charge amount of the cathode of thesecondary battery 110 to the estimated charge amount of the secondarybattery 110. The functional block that performs such an operation may bereferred to as a cathode charge amount estimator. The initial chargeamount of the cathode represents the charge amount of the cathode whenthe SOC of the cathode is 0. The initial charge amount of the cathodemay be predetermined and stored in the memory, or may be estimated bythe battery control apparatus 100 (or cathode charge amount estimator).

In addition, the battery control apparatus 100 may estimate the SOC ofthe cathode of the secondary battery 110 by dividing the estimatedcharge amount of the cathode of the secondary battery 110 by thecapacity of the cathode. The functional block that performs thisoperation may be referred to as a cathode SOC estimator.

Thereafter, the charge/discharge controller 102 receives a current ratiofrom the current ratio calculator 101, and the SOC estimate of thecathode of the secondary battery 110 from the battery control apparatus100 (or from the cathode SOC estimator). The charge/discharge controller102 controls the current passing through the secondary battery 110, orin other words the charge current and/or discharge current, based on thecurrent ratio corresponding to the SOC estimate of the cathode of thesecondary battery 110 and the capacities of the active material A andactive material B.

Specifically, the charge/discharge controller 102 may control thecurrent rate of the secondary battery 110 for charging and/ordischarging when the charge amount of the cathode of the secondarybattery 110 takes a certain value, based on the current ratio and thecapacities of the active material A and active material B.

For example the charge/discharge controller 102 may calculate thesubstantial charging/discharging rates of the active material A andactive material B, and reduce the charging/discharging rate of thesecondary battery 110 so that the substantial charging/discharging ratefor each active material will not exceed a threshold value. Thetolerance to a load may differ depending on the type of active material.The threshold value therefore may be determined in accordance with eachactive material. Specifically, the first threshold value, for example, 2C, may be applied to one active material, while the second thresholdvalue, for example, 3 C, may be applied to another active materialhaving a greater tolerance to a load.

The substantial charging/discharging rate of an active material may bederived from the product of the charging/discharging rate of thesecondary battery, the reciprocal of the ratio (e.g., 0.2, 0.4, 0.6, or0.8) of the capacity of this active material to the capacity of thecathode, and the ratio of the current passing through the activematerial to the current passing through the cathode. This represents theload on each active material. The ratio of the capacity of the activematerial A to the capacity of the cathode is Ca*Ma/(Ca*Ma+Cb*Mb), theratio of the capacity of the active material B to the capacity of thecathode is Cb*Mb/(Ca*Ma+Cb*Mb), the ratio of the current passing throughthe active material A to the current passing through the cathode isia/(ia+ib), and the ratio of the current passing through the activematerial B to the current passing through the cathode is ib/(ia+ib). Ca[mAh/g] denotes the capacity of the active material A per unit mass whenSOC is 0% to 100%, and Cb [mAh/g] denotes the capacity of the activematerial B per unit mass when SOC is 0% to 100%. In place of the ratioof the capacity of an active material, the ratio of the mass of theactive material may be adopted. For example, the ratio of the mass ofthe active material A to the mass of the cathode is Ma/(Ma+Mb), and theratio of the mass of the active material B to the mass of the cathode isMb/(Ma+Mb).

By calculating the charging rate of each active material in accordancewith the graph of FIG. 4 under a condition that a secondary batteryhaving a cathode prepared with multiple active materials of differentmixture ratios is charged at a constant rate of 1 C, the graph of FIG. 5is obtained.

The charge/discharge controller 102 may determine thecharging/discharging rate of the secondary battery 110 in accordancewith equation (8).

$\begin{matrix}{{R(S)} = \left\{ \begin{matrix}{R\; 0} & {\left( {{{case}\mspace{14mu}{{Ra}(S)}R\; 0} \leq {{Th}\mspace{14mu}{and}\mspace{14mu}{{Rb}(S)}R\; 0} \leq {Th}} \right)\mspace{14mu}} \\\frac{Th}{{Ra}(S)} & \left( {{{case}\mspace{14mu}{{Ra}(S)}R\; 0} > {{Th}\mspace{14mu}{and}\mspace{14mu}{{Ra}(S)}} \geq {{Rb}(S)}} \right) \\\frac{Th}{{Rb}(S)} & \left( {{{case}\mspace{14mu}{{Rb}(S)}R\; 0} > {{Th}\mspace{14mu}{and}\mspace{14mu}{{Rb}(S)}} \geq {{Ra}(S)}} \right)\end{matrix} \right.} & (8)\end{matrix}$

In equation (8), S denotes the SOC of the cathode, and R(S) denotes thetarget charging/discharging rate of the secondary battery 110 when thecathode SOC=S. R0 denotes a standard charging/discharging rate, such as1 C, that is adopted when the charging/discharging rate is notrestricted. Ra(S) and Rb(S) denote how many times greater thesubstantial charging/discharging rates of the active material A andactive material B, respectively, are than the charging/discharging rateof the secondary battery 110 when the cathode SOC=S, and Th denotes athreshold, such as 2 C. When the target charging/discharging rate is tobe complied with, the charging/discharging rate is restricted in the SOCregion within which the substantial charging/discharging rates of theactive material A and active material B would exceed the threshold valueif the standard charging/discharging rate is adopted. For the remainingSOC region, the standard charging/discharging rate can be adopted.

The charge/discharge controller 102 may determine the maximumcharging/discharging rates of the secondary battery 110 in accordancewith equation (9). If this is the case, the standardcharging/discharging rate may not be determined.

$\begin{matrix}{{R(S)} = \left\{ \begin{matrix}\frac{Th}{{Ra}(S)} & \left( {{{case}\mspace{14mu}{{Ra}(S)}} \geq {{Rb}(S)}} \right) \\\frac{Th}{{Rb}(S)} & \left( {{{case}\mspace{14mu}{{Rb}(S)}} \geq {{Ra}(S)}} \right)\end{matrix} \right.} & (9)\end{matrix}$

In the example of FIG. 5, if the threshold value is set to 2 C, thecharge/discharge controller 102 may determine the maximum charging rateof the secondary battery 110, as illustrated in FIG. 6. When the maximumcharging/discharging rate is to be complied with, thecharging/discharging rate can be increased as needed, within the rangeof the substantial charging/discharging rates of the active material Aand active material B not exceeding the threshold value.

Upon receipt of a command for charging/discharging the secondary battery110 at a rate that exceeds the target charging/discharging rate ormaximum charging/discharging rate from an upstream apparatus that is notshown, the charge/discharge controller 102 may control thecharging/discharging rate of the secondary battery 110 in such a mannerthat the charging/discharging rate will be smaller than or equal to thetarget charging/discharging rate or maximum charging/discharging rate.

The charge/discharge controller 102 may reduce the charging/dischargingrate of the secondary battery 110 so that the substantialcharging/discharging rate of each active material will not exceed thethreshold value. Depending on the specifications of the secondarybattery 110, however, the instantaneous value of the substantialcharging/discharging rate of the active material A or active material Bmay be allowed to exceed the threshold value. For example, thecharge/discharge controller 102 may reduce the charging/discharging rateof the secondary battery 110 so that the moving average of thesubstantial charging/discharging rates of each active material over thelatest certain period of time will not exceed the threshold value. Thisperiod of time may be determined based on the specifications of thesecondary battery 110.

In the examples of FIGS. 3 to 6, either one of the active material A andthe active material B is contained more in the mixture than the other,in all the cathodes. However, the charging/discharging rate may becontrolled in a similar manner for a cathode prepared by mixing the samecapacities of the active material A and the active material B, in thecapacity ratio of 1:1. FIG. 7 shows the substantial charging rates ofthe active material A and active material B, as well as the maximumcharging rate, when the secondary battery 110 includes the abovecathode.

According to FIG. 7, in the region of the charge amount being as low asapproximately 0 to 40 [mAh/g], the charge current passes mainly throughthe active material B so that the maximum charging rate of the secondarybattery 110 can be maintained around 1 C. On the other hand, in theregion of the charge amount being as high as approximately 60 to 120[mAh/g], the charge current passes mainly through the active material Aso that the maximum charging rate of the secondary battery 110 can bemaintained around 1.2 C. Even if there is no difference between thecapacities of the active material A and the active material B as shownabove, restricting the charge current of the secondary battery 110 whiletaking the load on each active material into consideration is ofimportance. Furthermore, depending on the combination of activematerials, the target charging/discharging rate or the maximumcharging/discharging rate when the current passes mainly through oneactive material may differ from the target charging/discharging rate orthe maximum charging/discharging rate when the current passes mainlythrough another active material. It would therefore be difficult torealize the charge/discharge control with the load on each activematerial suitably suppressed only by considering the capacity ratio ofactive materials in a mixed electrode and the region within which eachof these active materials mainly undergoes a charging reaction.

Next, the operation of the secondary battery system of FIG. 1 isexplained by referring to FIG. 8. First, the current ratio calculator101 sets parameters including the capacities of target active materials,and functions including an OCP function and its derivative for eachtarget active material (step S201). A target active material represents,for example, multiple active materials targeted for the calculation of acurrent ratio, such as the above mentioned active material A and activematerial B.

The current ratio calculator 101 sets the charge/discharge currentamount of the secondary battery 110, for example, the above mentionedvalue i (step S202). Furthermore, the current ratio calculator 101substitutes q0 for a variable q that expresses the charge amount of thetarget electrode for initialization (step S203). The target electrodehere denotes mixed electrode that includes target active materials. Thevalue q0 may be the initial charge amount of the target electrode, ormay take a larger value.

Steps S201, S202 and S203 may be executed in an order different fromFIG. 8, or in parallel. After steps S201 to S203, the process proceedsto step S204.

At step S204, the current ratio calculator 101 calculates the chargeamount of each of the target active materials, under the charge amountof the target electrode=q, so as to bring the OCPs of the target activematerials to be equal to each other, based on the parameters andfunctions set at step S201. At step S204, the above equation (2) orsimilar equation may be used.

Next, the current ratio calculator 101 calculates the current ratio ofthe target active materials based on the parameters and functionsdetermined at step S201, the charge/discharge current amount determinedat step S202, and the charge amount of the target active materialcalculated at step S204 (step S205). At step S205, the above equation(7) or similar equation may be used. The current ratio calculator 101stores the current ratio calculated at step S205 in the memory, inassociation with the value of the variable q (step S206).

After step S206, the current ratio calculator 101 determines whether thevariable q reaches q1 (step S207). Here, q1 may be a charge amountcorresponding to the target electrode SOC=100[%], or may be a valuesmaller than this. If it is determined that the variable q has reachedq1, the process proceeds to step S209. If not, the process proceeds tostep S208.

At step S208, the current ratio calculator 101 updates the variable q byadding Δq thereto. The value Δq may be a fixed value or a variablevalue. For example, Δq may be a value that changes in accordance withthe number of executions at step S207. After step S208, the processreturns to step S204.

At step S209, the charge/discharge controller 102 refers to the currentratios of the target active materials obtained by iterating the loop ofsteps S204 to S208 and stored in the memory, where the SOC of the targetelectrode takes various values, and based on these current ratios andthe capacity of the target active material determined at step S201, thecharge/discharge controller 102 controls the charge/discharge current ofthe secondary battery 110 when the SOC of the target electrode takesvarious values.

As explained above, the secondary battery system according to the firstembodiment controls the current passing through the secondary batterythat includes a mixed electrode containing different active materials.Specifically, this secondary battery system calculates the currentratios between active materials with the charge amount of the targetelectrode varied to different values, based on the capacities andcapacity-versus-potential properties of these active materials, andcontrols the current passing through the secondary battery when thecharge amount of the electrode has a certain value, based on the currentratio when the charge amount of the electrode has the certain value andthe capacity of each active material. At the time of charging anddischarging the secondary battery, the load on each of the activematerials included in the mixed electrode largely varies in accordancewith the charge amount of the electrode and the types and capacities ofthe active materials. The secondary battery system estimates the load,and controls the charging/discharging of the secondary battery inaccordance with the load on each active material. Thus, according tothis secondary battery system, the deterioration of the secondarybattery that includes the mixed electrode containing multiple activematerials can be suppressed.

Second Embodiment

The above mentioned secondary battery system according to the firstembodiment calculates the current ratio of currents passing throughmultiple active materials included in the target electrode, and controlsthe current passing through the secondary battery based on this currentratio, thereby suppressing the deterioration of the secondary batteryhaving such an electrode. In contrast, the secondary battery systemaccording to the second embodiment identifies, based on the currentratio, the charge amount (or SOC) region of the target electrode withinwhich a large load is applied to any active material of the electrode,for example the range of approximately 0 to 40 [mAh/g] indicated in FIG.7, and excludes such a region from the operational range of thesecondary battery. In this manner, the deterioration of the secondarybattery having a target electrode can be suppressed.

In a stationary secondary battery system, a hybrid electric vehicle(HEV), and plug-in HEV (PHEV), the range of the secondary battery fornormal operation may be determined to have a reduced rating capacity ofthe secondary battery. In such an application example, the deteriorationof the secondary battery can be suppressed without the need for controlof the charge/discharge current, by excluding the charge amount regionof the electrode within which a large load is applied to some of theactive materials included in the mixed electrode, from the operationalrange of the secondary battery.

As illustrated in FIG. 9, the secondary battery system according to thesecond embodiment includes a battery control apparatus 300, a secondarybattery 110, a load/power source 120, a current measurer 130, and avoltage measurer 140.

The battery control apparatus 300 may correspond to a processor andmemory in a manner similar to the above mentioned battery controlapparatus 100. Furthermore, in a manner similar to the battery controlapparatus 100, the battery control apparatus 300 calculates the currentratios of the current passing through different active materialscontained in the target electrode of the secondary battery 110 underdifferent charge amounts of the electrode of the secondary battery 110.The battery control apparatus 300 sets the operational range of thesecondary battery 110 based on the relationship between the chargeamount and the current ratio, for example, by excluding a certain chargeamount region from the operational range of the secondary battery 110.

Specifically, the battery control apparatus 300 includes a current ratiocalculator 101 and an operating range setter 302. The operating rangesetter 302 may be provided in a device that is positioned upstream withreference to the secondary battery system, such as HEV or PHEV, thatemploys the secondary battery 110. In a manner similar to the batterycontrol apparatus 100, the battery control apparatus 300 may estimatethe battery charge amount, the cathode/anode charge amount, and the SOCof the cathode/anode.

The operating range setter 302 receives the current ratio from thecurrent ratio calculator 101, and the SOC estimate of the targetelectrode of the secondary battery 110 from the battery controlapparatus 300 (or cathode/anode SOC estimator). The operating rangesetter 302 sets the operational region of the secondary battery 110,based on the current ratio corresponding to the SOC estimate of thetarget electrode of the secondary battery 110 and the capacity of thetarget active material included in the electrode.

Specifically, the operating range setter 302 may calculate thesubstantial charging/discharging rate of the target active material andexclude the charge amount range of the target electrode within which thesubstantial charging/discharging rate of each active material exceedsthe threshold value, from the operational range of the secondary battery110 in a manner similar to the above mentioned charge/dischargecontroller 102. The tolerance to a load may differ depending on the typeof active material. The threshold value therefore may be determined foreach active material. Specifically, the first threshold value, forexample, 2 C, may be applied to one active material, while the secondthreshold value, for example, 3 C, may be applied to another activematerial having a greater tolerance to a load.

The operating range setter 302 may conditionally exclude the chargeamount range of the target electrode within which the substantialcharging/discharging rate of an active material exceeds the thresholdvalue from the operational range of the secondary battery 110. In thismanner, the operational range can be avoided from becoming discontinuousor excessively narrowed. Furthermore, in such a charge amount range, thecharge/discharge control similar to the first embodiment may beperformed.

The operation of the secondary battery system in FIG. 9 is basically thesame as the operation indicated in FIG. 8. In place of step S209, or inaddition to this step, the step of the operating range setter 302setting the operational range of the secondary battery 110 is required.

As explained above, the secondary battery system according to the secondembodiment sets the operational range of the secondary battery having amixed electrode that includes different active materials so as to besmaller than the rating capacity of the secondary battery. Specifically,this secondary battery system calculates the current ratios betweenactive materials with the charge amount of the target electrode variedto different values, based on the capacities andcapacity-versus-potential properties of these active materials, and setsthe operational range of the secondary battery having the electrode,based on this current ratio and the capacity of each active material.The load applied to the active materials included in the mixed electrodeat the time of charging and discharging the secondary battery increasesin accordance with the charge amount of the electrode and types andcapacities of the active materials. The secondary battery systemestimates the load, and sets the operational range of the secondarybattery in accordance with the load on each active material. Thus,according to this secondary battery system, the deterioration of thesecondary battery that includes the mixed electrode containing multipleactive materials can be suppressed.

Third Embodiment

The above mentioned secondary battery system according to the secondembodiment suppresses the deterioration of the secondary battery, byexcluding the charge amount range of the electrode within which a largeload is applied to the active materials included in the targetelectrode, from the operational range of the secondary battery. Incontrast, the secondary battery according to the third embodiment isdesigned to have the cathode and anode having such potential propertiesthat the chargeable/dischargeable region will be arranged out of theabove charge amount range. Specifically, in this secondary battery, theelectrode paired with the target electrode is designed to have aninitial charge amount the value of which is larger than the abovementioned charge amount range. For example, if the cathode is the mixedelectrode, the anode will be designed in this manner.

In the above mentioned FIG. 5, for example, with the mixture ratio ofthe active material A and active material B being 8:2, the charging rateof the active material B exceeds 2 C when the SOC of the cathode iswithin the range of approximately 0 to 25[%] and approximately 95[%] andhigher. In view of this, the anode may be designed such that the chargeamount of the anode when SOC=0[%] approximately matches the chargeamount of the cathode when SOC=25[%]. Alternatively, the anode may bedesigned such that the charge amount of the anode when SOC=100[%]approximately matches the charge amount of the cathode when SOC=95[%].

It should be noted that, no matter how the charge amount range of theelectrode paired with the target electrode is designed, a considerableload may be applied, in part of the chargeable/dischargeable region ofthe secondary battery, to some of the active materials included in thetarget electrode. For this reason, the charge/discharge control similarto the first embodiment and/or setting of the operational region similarto the second embodiment may be adopted in such a charge amount range.

As discussed above, in the secondary battery according to the thirdembodiment, the electrode that is paired with the target electrode isdesigned to have potential properties so that thechargeable/dischargeable region of the secondary battery will bearranged out of the charge amount range of the target electrode, withinwhich the load on the active materials included in the electrodeincreases. Thus, the secondary battery can suppress the deterioration.

Fourth Embodiment

In the above mentioned first embodiment, the resistance of the targetactive material is not taken into consideration in the calculation ofthe current ratio. In the secondary battery system according to thefourth embodiment, the charge/discharge controller 102 takes theresistance of the target active material into consideration to furtheraccurately calculate the current ratio of the active materials.

In consideration of the resistance of the active material, the targetelectrode can be represented as a circuit model illustrated in FIG. 10.To simplify the explanation, the target electrode denotes a cathodeprepared by mixing the active material A and active material B asdescribed in the first embodiment. In FIG. 10, Ra and Rb denote theresistances of the active material A and active material B,respectively. Furthermore, fa(Qa) and fb(Qb) denote the OCP for theactive material A and for the active material B, respectively.

The resistance Ra and resistance Rb may be determined in advance.However, as discussed later in the fifth embodiment, these resistancesmay be estimated and updated as the deterioration of the secondarybattery 110 advances. The resistance Ra may be determined, for example,as a value proportional to the reciprocal of the capacity (Ca*Ma) of theactive material A. Similarly, the resistance Rb may be determined as avalue proportional to the reciprocal of the capacity (Cb*Mb) of theactive material B.

FIG. 10 shows a parallel circuit. This means that the sum of the OCP ofthe active material A and the voltage drop caused by the resistance ofthe active material A is equal to the sum of the OCP of the activematerial B and the voltage drop caused by the resistance of the activematerial B. In other words, equation (10) is established.

$\begin{matrix}{{fa}{{\left( \frac{Qa}{Ma} \right) + {iaRa}} = {{f{b\left( \frac{Qb}{Mb} \right)}} + {ibRb}}}} & (10)\end{matrix}$

It is assumed here that a charge/discharge current is passed over ashort time period Δt. During this time, the charge amount of the cathodechanges from Q to Q+iΔt. Concurrently, the charge amount of the activematerial A changes from Qa to Qa+iaΔt, and the charge amount of theactive material B changes from Qb to Qb+ibΔt. Here, ia and ib denote thesizes of currents that pass through the active material A and activematerial B, respectively, during the short time period Δt. The ratioia:ib is the current ratio calculated by the current ratio calculator101.

The following equation (11) is derived by the first order approximation.

$\begin{matrix}{{{{fa}\left( \frac{Qa}{Ma} \right)} + {\frac{ia\Delta t}{Ma}{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}} + {iaRa}} = {{f{b\left( \frac{Qb}{Mb} \right)}} + {\frac{ib\Delta t}{Mb}{fb}^{\prime}\;\left( \frac{Qb}{Mb} \right)} + {ibRb}}} & (11)\end{matrix}$

Equation (11) can be simplified as follows:

$\begin{matrix}{{\begin{bmatrix}{H\; 1} & {H\; 2} \\1 & 1\end{bmatrix}\begin{bmatrix}{ia} \\{ib}\end{bmatrix}} = {{\begin{bmatrix}{H3} \\i\end{bmatrix}H\; 1} = {{{\frac{\Delta t}{Ma}{{fa}^{\prime}\left( \frac{Qa}{Ma} \right)}} + {{Ra}{H\; 2}}} = {{{- \left( {{\frac{\Delta t}{Mb}{{fb}^{\prime}\left( \frac{Qb}{Mb} \right)}} + {Rb}} \right)}H\; 3} = {{{fb}\left( \frac{Qb}{Mb} \right)} - {{fa}\left( \frac{Qa}{Ma} \right)}}}}}} & (12)\end{matrix}$

By solving these simultaneous equations, the current ratio as expressedby equation (13) can be obtained.

$\begin{matrix}{{{ia}\text{:}ib} = {\frac{{H3} - {H2i}}{{H\; 1} - {H\; 2}}\text{:}\frac{{{- H}3} + {H1i}}{{H1} - {H2}}}} & (13)\end{matrix}$

When the current ratios are calculated in the above manner for thecathodes having different mixture ratios as exemplified in FIG. 3, thegraph of FIG. 11 can be obtained. In the example of FIG. 11, it isassumed that charging starts in the vicinity of the cathode SOC=0[%],and the resistances Ra and Rb are proportional to the reciprocal of thecapacity Ma of the active material A and the reciprocal of the capacityMb of the active material B, respectively.

As explained above, the secondary battery system according to the fourthembodiment differs from the secondary battery system according to thefirst embodiment in that the resistances of the target active materialsare further taken into consideration when calculating the current ratioof the active materials. Thus, according to the present secondarybattery system, the loads applied on the active materials that areincluded in the mixed electrode at the time of charging and dischargingthe secondary battery can be further accurately estimated, and employedfor the charge/discharge control of the secondary battery and/or forsetting the operational range of the secondary battery. As a result,according to this secondary battery system, the deterioration of thesecondary battery that includes the mixed electrode containing multipleactive materials can be suitably suppressed.

For the secondary battery system according to the second embodiment, theoperational range of the secondary battery may be set by using thecurrent ratio calculated by the scheme explained in the presentembodiment. In addition, the secondary battery according to the thirdembodiment may be designed by using the current ratio calculated by thescheme explained in the present embodiment.

Fifth Embodiment

The secondary battery system according to the fifth embodiment canreduce errors in the current ratio by adopting regression calculationfor estimation of part of the parameters that are used for thecalculation of the current ratio described above in the first and fourthembodiments.

Specifically, as illustrated in FIG. 12, the secondary battery systemaccording to the fifth embodiment includes a battery control apparatus400, a secondary battery 110, a load/power source 120, a currentmeasurer 130, and a voltage measurer 140.

In a manner similar to the above mentioned battery control apparatus100, the battery control apparatus 400 calculates the current ratios ofthe currents passing through different active materials included in theelectrode of the secondary battery 110 under different charge amounts ofthe target electrode of the secondary battery 110. Based on therelationship between the charge amount and the current ratio, thebattery control apparatus 400 controls the current passing through thesecondary battery 110 so that, for example, the charging rate and/ordischarging rate of the secondary battery 110 can be reduced within acertain charge amount region.

In particular, the battery control apparatus 100 includes a currentratio calculator 401, a charge/discharge controller 102, and an internalstate calculator 403.

As part or all of the parameters including capacities and/or resistancesof the active material A and/or active material B, the current ratiocalculator 401 uses the calculation results obtained by the internalstate calculator 403. By using these parameters, the current ratiocalculator 401 may perform the same or similar calculation to thecalculation performed by the current ratio calculator 101.

The internal state calculator 403 performs the regression calculationbased on the input data stored in the memory, such as measured orpredicted current values and/or measured or predicted power values, andalso measured or predicted (battery) voltage values. Based on the resultof this regression calculation, the internal state calculator 403updates at least part of the parameters stored in the memory.

The internal state calculator 403 may update the estimated capacities ofthe cathode/anode active materials, estimated cathode/anode initialcharge amounts, and/or estimated internal resistance of the secondarybattery (which may include resistance of each active material), based onthe current and voltage values measured or predicted at multiple timepoints during the constant current charging by using the techniquedisclosed, for example, in JP-A 2015-111086 (KOKAI) or any similartechnique.

Next, the operation of the secondary battery system of FIG. 12 isexplained by referring to FIG. 13. First, the current ratio calculator401 sets functions including an OCP function and its derivative for eachtarget active material (step S501).

The internal state calculator 403 performs the regression calculationbased on the above mentioned input data, and estimates the capacity foreach target active material (step S502). At step S502, the internalstate calculator 403 may estimate the capacities of part of the targetactive materials so that the capacities of the remaining activematerials do not have to be estimated. In addition, at step S502, theinternal state calculator 403 may estimate the resistances of part orall of the target active materials.

Furthermore, the current ratio calculator 401 sets the charge/dischargecurrent amount of the secondary battery 110, for example, the abovementioned value i (step S202), and initializes a variable q thatexpresses the charge amount of the target electrode by substituting q0for the variable (step S203).

Steps S501, S502, S202 and S203 may be executed in an order differentfrom FIG. 13, or in parallel. The process at step S204 and after may bethe same as or similar to FIG. 8, and thus is omitted from theexplanation.

The secondary battery system according to the fifth embodiment adoptsregression calculation to estimate and update part or all of theparameters used for the calculation of the current ratio described abovein the first and fourth embodiments. In this manner, the secondarybattery system can suppress errors in the current ratio, which tend tobe caused when the actual internal state of the secondary battery fromthe parameters determined at the time of designing the secondary batterydiverge in accordance with the deterioration of the secondary battery.

For the secondary battery system according to the second embodiment, theoperational range of the secondary battery may be set by using thecurrent ratio calculated by the scheme explained in the presentembodiment. In addition, the secondary battery according to the thirdembodiment may be designed by using the current ratio calculated by thescheme explained in the present embodiment.

Sixth Embodiment

The fifth embodiment may be applicable to an assembled battery systemhaving an assembled battery that contains multiple secondary batteriescoupled to each other in parallel or in series.

Each of the secondary batteries contained in the assembled battery isconfigured to include a mixed electrode as explained in the aboveembodiments. However, the parameters such as the capacities of theactive materials may not always be uniform among secondary batteries dueto errors at the time of production and deterioration over time.

These secondary batteries are divided into battery modules. A batterymodule may include one secondary battery or multiple secondarybatteries.

The assembled battery system according to the sixth embodiment mayinclude, in addition to such an assembled battery, a battery controlapparatus, a load/power source 120, a current measurer 130, and avoltage measurer 140. The battery control apparatus includes a currentratio calculator, an internal state calculator, and a charge/dischargecontroller.

This current ratio calculator calculates the current ratio for everybattery module in a manner similar to the above mentioned current ratiocalculator 401. The current ratio calculator may calculate, based on thecapacity and the capacity-versus-potential properties of the activematerial A of a secondary battery included in a battery module and thecapacity and the capacity-versus-potential properties of the activematerial B of this secondary battery, the current ratios of the currentpassing through the active material A of the secondary battery and thecurrent passing through the active material B of the secondary batterywhen the charge amount of the cathode of the secondary battery ischanged to take different values.

Furthermore, this internal state calculator updates parameters includingthe capacities of the active materials and the resistances of the activematerials for each battery module, in a manner similar to the internalstate calculator 403. The internal state calculator may performregression calculation, based on the input data including (a) thecurrent/power measurement values measured at multiple time points duringthe time of charging and discharging a battery module, and/or (b) theestimate current/power values at multiple time points during the time ofcharging and discharging the battery module, and update the capacity ofthe active material A of the secondary battery included in the batterymodule and the active material B of the secondary battery.

Furthermore, this charge/discharge controller determines the(recommended) charging/discharging rate for every battery module in amanner similar to the above charge/discharge controller 102. Thecharging/discharging rate, however, cannot be controlled for eachbattery module, but an assembled battery needs to be controlled as awhole. The charge/discharge controller therefore determines thecharging/discharging rate of the assembled battery based on therecommended charging/discharging rates that are determined for themultiple battery modules, based on which the charge/discharge controllercontrols the charging/discharging rate of the assembled battery. Thischarge/discharge controller differs from the above mentionedcharge/discharge controller 102 in this respect.

For example, the charge/discharge controller may determine therecommended charging/discharging rate of the battery module when thecharge amount of the cathode of the secondary battery takes the firstvalue, based on the capacity of the active material A of the secondarybattery included in the battery module, the capacity of the activematerial B of the secondary battery, and the current ratio when thecharge amount of the cathode of the secondary battery takes the firstvalue. The charge/discharge controller may control thecharging/discharging rate of the assembled battery, based on statisticalvalues of the recommended charging/discharging rates determined for themultiple battery modules such as the minimum value, average value,median value, and mode. Alternatively, the charge/discharge controllermay select the most deteriorated battery module, such as a batterymodule for which the parameter calculated by the internal statecalculator most diverges from the initial value, and control thecharging/discharging rate of the assembled battery by using therecommended charging/discharging rate determined for the selectedbattery module.

As discussed above, the assembled battery system according to the sixthembodiment determines the recommended charging/discharging rate for eachof the battery modules obtained by dividing secondary batteries includedin the assembled battery in a manner similar to the fifth embodiment,and further determines the charging/discharging rate of the assembledbattery based on the recommended charging/discharging rates determinedfor these battery modules. Thus, this assembled battery system cansuppress the deterioration of the assembled battery containing not onlyone battery module but also multiple battery modules.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel methods and systems describedherein may be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the methods andsystems described herein may be made without departing from the spiritof the inventions. The accompanying claims and their equivalents areintended to cover such forms or modifications as would fall within thescope and spirit of the inventions.

What is claimed is:
 1. A secondary battery system comprising: a secondary battery comprising a first electrode including a first active material and a second active material, and a second electrode including at least a third active material; a current ratio calculator configured to calculate a current ratio of a current passing through the first active material and a current passing through the second active material for each of different values of a charge amount of the first electrode, based on a capacity and capacity-versus-potential properties of the first active material and a capacity and capacity-versus-potential properties of the second active material; and a controller configured to, based on the capacity of the first active material, the capacity of the second active material and the current ratio when the charge amount of the first electrode takes a first value, control the current passing through the secondary battery when the charge amount of the first electrode indicates the first value.
 2. The system according to claim 1, wherein the controller restricts a current rate for at least one of charging and discharging the secondary battery when the charge amount of the first electrode takes the first value, based on the capacity of the first active material, the capacity of the second active material, and the current ratio when the charge amount of the first electrode takes the first value.
 3. The system according to claim 1, wherein the controller calculates a first ratio of the current passing through the first active material to the current passing through the first electrode when the charge amount of the first electrode takes the first value, based on the current ratio when the charge amount of the first electrode takes the first value, and reduces a current rate for charging and/or discharging the secondary battery when the charge amount of the first electrode takes the first value on condition of a product of (a) the first ratio, (b) a reciprocal of a second ratio of the capacity of the first active material to a capacity of the first electrode, and (c) charging rate or discharging rate of the secondary battery, exceeding a threshold value.
 4. The system according to claim 1, wherein the current ratio calculator calculates the current ratio, based further on a first function that returns a potential of the first active material with a charge amount of the first active material per unit mass as an argument and a second function that returns a potential of the second active material with a charge amount of the second active material per unit mass as an argument.
 5. The system according to claim 1, wherein the current ratio calculator calculates the current ratio, based further on a resistance of the first active material and a resistance of the second active material.
 6. The system according to claim 1, further comprising an internal state calculator configured to perform regression calculation based on input data including at least one of (a) measurement values of currents and/or powers measured at a plurality of time points during charging and/or discharging the secondary battery and (b) estimated values of currents and/or powers at a plurality of time points during charging and/or discharging the secondary battery, and to update the capacity of the first active material and the capacity of the second active material.
 7. A secondary battery comprising: a first electrode including a first active material and a second active material; and a second electrode including at least a third active material, wherein an initial charge amount of the second electrode is larger than an initial charge amount of the first electrode, and in at least part of a range in which the charge amount of the first electrode is smaller than the initial charge amount of the second electrode, a product of (a) a first ratio of a current passing through the first active material to a current passing through the first electrode, (b) a reciprocal of a second ratio of a capacity of the first active material to a capacity of the first electrode, and (c) a charging rate or discharging rate of the secondary battery, exceeds a threshold value.
 8. An assembled battery system comprising an assembled battery that includes a plurality of secondary batteries coupled in parallel or in series, wherein each of the secondary batteries includes a first electrode including a first active material and a second active material, and a second electrode including at least a third active material, and the system further comprises: an internal state calculator configured to perform regression calculation for each of a plurality of battery modules obtained by dividing the secondary batteries, based on input data including at least one of (a) measurement values of currents and/or powers measured at a plurality of time points during charging and/or discharging each battery module and (b) estimated values of currents and/or powers at a plurality of time points during charging and/or discharging the battery module, and to update a capacity of the first active material of the secondary battery included in the battery module and a capacity of the second active material of the secondary battery; a current ratio calculator configured to calculate for each of the battery modules and for each of different values of a charge amount of the first electrode of the secondary battery included in the battery module a current ratio of a current passing through the first active material of the secondary battery and a current passing through the second active material of the secondary battery, based on the capacity and capacity-versus-potential properties of the first active material of the secondary battery and the capacity and capacity-versus-potential properties of the second active material of the secondary battery; and a controller configured to determine a recommended current rate, for each of the battery modules, for charging and/or discharging the battery module when the charge amount of the first electrode of the secondary battery included in the battery module takes a first value, based on (a) the capacity of the first active material of the secondary battery, (b) the capacity of the second active material of the secondary battery, and (c) the current ratio when the charge amount of the first electrode of the secondary battery takes the first value, and to control a current passing through the assembled battery, based on the recommended current rate determined for each of the battery modules.
 9. The system according to claim 8, wherein the controller controls a current rate for charging and/or discharging the assembled battery, using a statistical value of the recommended current rate determined for each of the battery modules.
 10. The system according to claim 8, wherein the controller selects one of the battery modules based on a degree of divergence with respect to an initial value of the capacity of the first active material and/or the capacity of the second active material updated for the battery modules, and controls a current rate for charging and/or discharging the assembled battery, using a recommended current rate determined for the selected battery module. 